Time and Work problems
- 1. A can do a piece of work in 10 days ,B can do it in 15 days. Working together they can finish the work in?
Options- A. 9
- B. 8
- C. 10
- D. 6 Discuss
Correct Answer: 6
Explanation:
Efficiency of A = 10%
Efficiency of B = 6.66%
? Required number of days = 100/16.66 = 6 days
- 2. A can do a piece of work in 24 days, while B can do it in 30 days. With the help of C they can finish the whole work in 12 days.How much time is required for C to complete the work, alone?
Options- A. 100 days
- B. 120 days
- C. 125 days
- D. 72 days Discuss
Correct Answer: 120 days
Explanation:
Efficiency of A = 100/24 = 4.16%
Efficiency of B = 100/30 = 3.33%
Efficiency of (A+ B+C) =100/12 = 8.33%
? Efficiency of C = (8.33) - (4.16 + 3.33) = 0.83%
? Number of days required by C to complete the work alone
= 100/0.83 = 100/(5/6) = 120 days
(Note : 5/6 = 0.833)
- 3. A is thrice efficient as B and C is twice as efficient as B. what is the ratio of number of days taken by A,B and C , when they work individually?
Options- A. 2 : 6 : 3
- B. 2 : 3 : 6
- C. 1 : 2 : 3
- D. 3 : 1 : 2 Discuss
Correct Answer: 2 : 6 : 3
Explanation:
A : B : C
Ratio of efficiency 3 : 1 : 2
Ratio of number of days { 1/3 : 1/1 : 1/2 }
or 2 : 6 : 3
Hence, (a) is correct [ Time = 1/ Efficiency ]
- 4. If A takes 4/5 days as B takes and working together they require 20/3 days to complete the whole work. What is the efficiency of B?
Options- A. 62/3%
- B. 16%
- C. 5.55%
- D. 81/3% Discuss
Correct Answer: 62/3%
Explanation:
Efficiency of A + B = 100/(20/3) = 15%
No. of days ( A:B ) = 4 : 5
Efficiency ( A:B ) = 5 : 4
? Efficiency of B = (4/9) x 15 = 20/3 = 62/3%
- 5. A is thrice as efficient as B. Working together they complete the work in 3 days. If B take 8 days more then A, What is the number of days taken by A to finish the while work, alone?
Options- A. 4
- B. 2
- C. 12
- D. 16 Discuss
Correct Answer: 4
Explanation:
Efficiency of A + B = 33.33% = 100/3
Ratio of efficiency of A and B = 3 : 1
? Efficiency of A = (3/4) x 33.33 = 25%
? Number of days taken by A = 100/25 = 4
- 6. A and B can do a piece of work in 12 days B and C in 15 days C and A in 20 days. In how many days can C alone do it?
Options- A. 60
- B. 50
- C. 25
- D. 24 Discuss
Correct Answer: 60
Explanation:
Efficiency of (A + B) = 8.33%
Efficiency of (B + C) = 6.66%
Efficiency of (C + A) = 5.00%
? Efficiency of A + B + C = (8.33 + 6.66 + 5) / 2 = 10%
? Efficiency of C = Efficiency of [(A + B + C) - (A + B) ]
= (10 - 8.33) = 1.66%
? No. of days required by C alone = 100/1.66 = 60days
- 7. A and B can do a piece of work in 8 days, B and C can do the same work in 12 days and A and C complete it in 8 days. In how many days A, B and C can complete the whole work,working together?
Options- A. 4
- B. 6
- C. 12
- D. 9 Discuss
Correct Answer: 6
Explanation:
Efficiency of (A + B) = 12.5%
Efficiency of (B + C) = 8.33%
Efficiency of (C + A) = 12.5%
? Efficiency of [(A + B) + (B + C) + (C + A)] = 33.33%
? Efficiency of (A + B + C) = 16.66%
? No. of days Required by A, B and C together = 100/16.66 = 6 days
- 8. A, B and C working in a garment manufacturing company can do the same assignment in 24, 6 and 12 days, respectively. Working together the assignment will be complete in how many days?
Options- A. 33/7 days
- B. 43/7 days
- C. 4 days
- D. 3 days Discuss
Correct Answer: 33/7 days
Explanation:
(A + B + C)' S 1 day's work = (1/24) + (1/6) + (1/12) = 7/24
? (A + B + C) can do the entire work in = 24/7
= 33/7 days
- 9. A women can weave a basket in 6 days. But with the help of her daughter, she can complete the work in 4 days. In what time can the daughter alone do the work?
Options- A. 12 days
- B. 16 days
- C. 8 days
- D. 10 days Discuss
Correct Answer: 12 days
Explanation:
Women's 1 day's work = 1/6
(Women + Daughter)'s 1 day's work = 1/4
? Daughter's 1 day's work = 1/4 - 1/6 = 1/12
So, the daughter can do the work in 12 days.
- 10. Working together P and Q can do a job is 6 days. Q and R can do the same job in 10 days while P and R can do it in 5 days. How long will it take, if all of them work together to complete the job?
Options- A. 42/7 days
- B. 43/7 days
- C. 44/7 days
- D. 45/7 days Discuss
Correct Answer: 42/7 days
Explanation:
(P + Q)'S 1 day's work = 1/6
(Q + R)'s 1 day's work = 1/10
(P + R)'s 1 day's work = 1/5
On adding, 2 (P + Q + R)'s 1 day's work = 1/6 + 1/10 + 1/5 = 7/15
( P + Q + R)'s 1 day's work = 7/30
? (P + Q + R)'s can do the entire work in = 30/7 = 42/7 days
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